Adding and Subtracting Rational Expressions

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials.

Front

How do you add rational expressions with the same denominator?

Back

To add rational expressions with the same denominator, combine the numerators and keep the denominator the same: \( \frac{a}{c} + \frac{b}{c} = \frac{a + b}{c} \).

Front

What is the first step in adding rational expressions with different denominators?

Back

The first step is to find a common denominator for the rational expressions.

Front

How do you subtract rational expressions with the same denominator?

Back

To subtract rational expressions with the same denominator, subtract the numerators and keep the denominator the same: \( \frac{a}{c} - \frac{b}{c} = \frac{a - b}{c} \).

Front

What is the least common denominator (LCD)?

Back

The least common denominator (LCD) is the smallest multiple that is common to the denominators of two or more fractions.

Front

How do you find the LCD of \( \frac{1}{x} \) and \( \frac{1}{x^2} \)?

Back

The LCD of \( \frac{1}{x} \) and \( \frac{1}{x^2} \) is \( x^2 \).

Front

What is the process for adding \( \frac{2}{x} + \frac{3}{x^2} \)?

Back

1. Find the LCD, which is \( x^2 \). 2. Rewrite \( \frac{2}{x} \) as \( \frac{2x}{x^2} \). 3. Add: \( \frac{2x + 3}{x^2} \).

Front

What happens when you add rational expressions with unlike denominators?

Back

You must first convert each expression to have a common denominator before adding.

Front

What is the formula for adding two rational expressions \( \frac{a}{b} + \frac{c}{d} \)?

Back

The formula is: \( \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \).

Front

How do you simplify the expression \( \frac{2x}{x^2} + \frac{3}{x^2} \)?

Back

Combine the numerators: \( \frac{2x + 3}{x^2} \) and simplify if possible.